import java.awt.geom.*;

// 边框
Rectangle2D.Double border = new Rectangle2D.Double(.....);

// 中间的横纵线
Line2D.Double hline1 = new Line2D.Double(...);
Line2D.Double hline2 = ....
...
Line2D.Double hlineN = ....
Line2D.Double vline1 = ....
Line2D.Double vline2 = ....
...
Line2D.Double vlineN = ....

// 组合起来
Area board = new Area(border);
board.add(new Area(hline1));
....
board.add(new Area(vlineN));

// paint
Graphics2D g2d = (Graphics2D)g;
g2d.setPaint(Color.BLACK);

g2d.draw(board);

------解决方案--------------------
记得我做的时候，是在一张背景图上画好线（如果背景图上有线的话难以把握位置），再根据坐标及行列间距计算出落子位置即可